CN103616802B - Method for measuring projection objective wave aberration of photo-etching machine - Google Patents

Abstract

The invention discloses a method for detecting wave aberration of a projection type photo-etching machine imaging system. The method comprises the following steps: establishing a quick positive model of the photo-etching machine imaging system, analyzing and resolving a Zernike coefficient sensitivity matrix, optimizing and resolving a detection mask pattern and resolving the wave aberration measured on the basis of a single light intensity. Through the method, the wave aberration measured on the basis of a single defocus space image light intensity can be detected by analyzing and resolving a space image light intensity value and the Zernike coefficient sensitivity matrix without the aberration.

Description

A kind of measuring method of wave aberration of photo-etching machine projection objective

Technical field

The invention belongs to projection aligner's imaging system fields of measurement, be specifically related to a kind of measuring method of wave aberration of photo-etching machine projection objective.

Background technology

In nanometer manufactures, in order to realize the high precision etching of optical lithography, need every photoetching technique indexs such as assessment image forming quality of photoetching machine, photoetching resolution and characteristic dimension homogeneity.Wave aberration of photo-etching machine projection objective (Wavefront Aberration) is the important indicator affecting advanced scanning projecting photoetching machine performance, directly have influence on above-mentioned every photoetching technique index, therefore wave aberration of photo-etching machine projection objective is one of Testing index of most critical in litho machine.

Wave aberration refers to the optical path difference between the actual corrugated after projection objective and desirable corrugated, can characterize with zernike polynomial and coefficient thereof.Along with continuous progress and the development of resolution enhance technology, positive its manufacturing limit of Step wise approximation of numerical aperture (NA, Numerical Aperture) of projection lens of lithography machine.Such as, the NA value of current dry lithography machine projection objective reaches more than 0.85; Adopt immersion type photoetching, then NA reaches more than 1.0.Under ultra-high numerical aperture, for ensureing the key indexs such as image quality, photoetching resolution and characteristic dimension homogeneity, require that the wave aberration of projection objective is less than 10m λ (namely for 193nm deep knowledge base lighting source, wave aberration should be less than 2nm), this just requires that wave aberration zernike coefficient accuracy of detection reaches 2m λ; And only the lower-degree coefficient obtained in zernike polynomial is far from being enough, needs the zernike coefficient obtaining higher exponent number, generally will reach 37 grades (i.e. Z37) simultaneously.Thus very stern challenge is proposed to wave aberration detection technique and system thereof.Wave aberration online measuring technique, to be integrated in based on the aerial image sensor on work stage or silicon chip, realizes the direct measurement of projection objective aerial image, thus passes through the real-time process of measurement data, reconstructs the wave aberration of projection objective rapidly and accurately.

At present, in wave aberration detection, a kind of conventional method is detected by interference exactly.As ILIAS (the Integrated Lens Interferometer At Scanner) technology of ASML company, iPot (the Integrated Projecting Optics Tester) technology of Nikon company and SPIN (the SlantProjection through a Pinhole) technology of Canon company and LDI (Line Diffraction Interferometer) technology.When using interference to carry out wave aberration measurement, integrated interferometer or portable interferometer, therefore cost is higher, and hardware design is complicated.This kind of detection technique can obtain 37 grades of Zernike coefficients, and it is even higher that precision can reach 2m λ, and detection time is relatively short, and robustness is high.But this kind of technology is due to system, and particularly hardware design is quite complicated, and have suitable difficulty, applicability is not high.

The online wave aberration another kind of method detected wherein is TAMIS (the TIS AtMultiple Illumination Settings) technology of ASML company, utilize transmission image-position sensor TIS (TransmissionImage Sensor) spin-scanning alignment Procedure Acquisition aerial image actual coordinate and relative to the transverse direction of theoretical image space or longitudinal bias, coordinate the automatic regulation function of litho machine logarithm value aperture NA and partial coherence factor σ, by calculating the wave aberration of projection objective based on the sensitivity model of experience.Because TAMIS technology is only confined to the linear relationship analyzing light intensity signal and geometrical offset in spatial domain, this linear model is the experience linear model simplified, its linearity must receive the impact of lighting system and mask label size, therefore, TAMIS technology can only detect wave aberration low order Zernike coefficient, is difficult to adapt to further developing of current litho machine height NA and low CD.

Summary of the invention

For the deficiencies in the prior art, the object of the present invention is to provide a kind of measuring method for wave aberration of photo-etching machine projection objective, adopt based on the wave aberration method for quick of single luminous intensity measurement, realize little wave aberration quick, accurately extract, and flow process realizes simple.

The measuring method of a kind of wave aberration of photo-etching machine projection objective provided by the invention, for carrying out in situ detection fast to the less wave aberration of projection objective, said method comprising the steps of:

Step 102, determine the characterisitic parameter exposed according to actual litho machine process conditions, wherein, characterisitic parameter comprises litho machine numerical aperture, the wavelength of light source, shape and other light sources parameter;

Step 104, theoretical according to lithographic projection, when wavelength difference is less, simplify lithographic projection forward model;

Step 106, according to the forward model after simplification, calculates light intensity value during sensitivity matrix and the aberrationless of zernike coefficient, wherein, and the matrix that sensitivity matrix is made up of the sub-matrix that each zernike coefficient is corresponding;

Step 108, adopts the conditional number of sensitivity matrix to carry out mask graph optimization as objective function to the parameter of mask graph, obtains optimum mask;

Step 110, adopts the mask graph optimized and obtain, and carries out actual exposure measure light intensity at certain out of focus place;

Step 112, according to exposing the light intensity value that obtains, and the aberrationless light intensity value calculated and sensitivity matrix, solve zernike coefficient, obtain the wave aberration reconstructed.

Compared with the method detected with existing wave aberration, the small echo aberration measurement method based on single luminous intensity measurement provided by the present invention is a kind of easy, in-situ measuring method of more easily realizing.First, the present invention is in the process of carrying out Forward modeling, achieve the extraction completely to zernike coefficient, the zernike coefficient characterizing wave aberration to be separated out as variable completely, sensitivity matrix is as needing complicated calculations and part consuming time in a large number, only need to calculate in advance once, do not need repeatedly to calculate in a large number in measuring process; Secondly, the present invention proposes the Analytical Expression form of sensitivity matrix, thus the zernike coefficient of wave aberration directly can be calculated by least square method, avoid in the optimized algorithm process by iteration the problem repeatedly calling complicated forward model, avoid in iterative process the problem being absorbed in local optimum simultaneously, make the measurement of wave aberration more simple.

Accompanying drawing explanation

With reference to explanation below, by reference to the accompanying drawings, best understanding can be had to the present invention.

Fig. 1 shows the process flow diagram measured according to wave aberration of photo-etching machine projection objective of the present invention;

Fig. 2 shows the mask graph of four kinds of exemplary different topology structures;

Fig. 3 shows the mask graph optimum results of four kinds of exemplary different topology structures;

Conditional number before and after the mask graph optimization that Fig. 4 shows four kinds of exemplary different topology structures compares;

Fig. 5 shows the zernike coefficient results contrast that an exemplary wave aberration detects;

Fig. 6 shows the error of the zernike coefficient that an exemplary wave aberration detects.

Embodiment

In order to make object of the present invention, technical scheme and advantage clearly understand, below in conjunction with accompanying drawing and exemplary embodiment, the present invention will be described in further detail.Should be appreciated that exemplary embodiment described herein only in order to explain the present invention, protection scope of the present invention is not by the restriction of these embodiments.

Fig. 1 shows the detection method treatment scheme 100 of wave aberration of photo-etching machine projection objective provided by the invention, and it can be used for carrying out in situ detection to the wave aberration of projection objective.Concrete operations flow process is as follows:

S102, determines the characterisitic parameter exposed according to actual litho machine process conditions;

For projection aligner, characterisitic parameter comprises litho machine numerical aperture, the wavelength of light source, shape and other light sources parameter.The shape of wherein said light source comprises circle, annular, secondary light source and level Four light source, and other light sources parameter comprises partial coherence factor σ _out, σ _inand the parameter such as azimuth angle theta.

Before measurement wave aberration of photo-etching machine projection objective, need the actual exposure parameter determining this litho machine.

S104, theoretical according to lithographic projection, simplify lithographic projection forward model

According to Thelma Hopkins image-forming principle, aerial image light distribution I (x; H) be about intersection transport function T (f on emergent pupil face ₁, f ₂; And the double integral of mask frequency domain information O (f) h):

I(x;h)＝∫∫O(f ₁)O ^*(f ₂)T(f ₁,f ₂;h)×exp[-2πi(f ₁-f ₂)·x]df ₁df ₂， (1)

Wherein x is spatial domain coordinate, and f is frequency domain coordinates, and h is defocusing amount, and * is complex conjugate.And intersect transport function be one about light source J (f) and pupil function H (f; H) four-dimensional transmission factor:

T(f ₁,f ₂;h)＝∫J(f)H(f+f ₁;h)H ^*(f+f ₂;h)df. (2)

Based on the equation of the partially coherent image formation system of Thelma Hopkins, can by pupil function H (f; H) the wave aberration item zernike polynomial R in _nf () characterizes:

$H(f;h)=P(f;h)\exp [-\mathrm{ik}\underset{n}{\mathrm{\Σ}}{Z}_n{R}_n\left(f\right)],---\left(3\right)$

Wherein, P (f; H)=circ (| f|) is the pupil function without wave aberration, Z _nfor characterizing the zernike coefficient of wave aberration.Intersection transport function is carried out Taylor expansion to single order item:

$T(f_1,f_2;h)=T_0(f_1,f_2;h)+T_1(f_1,f_2;h)=T_0(f_1,f_2;h)+\underset{n}{\mathrm{\Σ}}{Z}_n{B}_n(f_1,f_2;h),---\left(4\right)$

Wherein, T ₀(x; And B h) _n(x; H) can be expressed as

T ₀(f ₁,f ₂;h)＝∫J(f)P(f+f ₁;h)P ^*(f+f ₂;h)df, (5)

B _n(f ₁,f ₂;h)＝-ik∫J(f)P(f+f ₁;h)P ^*(f+f ₂;h)×[R _n(f+f ₁)-R _n(f+f ₂)]df. (6)

Bring this first order modeling into (1) formula again, the single order relation between aerial image light intensity and zernike coefficient can be obtained:

$I(x;h)=I_0(x;h)+I_1(x;h)=I_0(x;h)+\underset{n}{\mathrm{\Σ}}{Z}_n{A}_n(x;h),---\left(7\right)$

In formula, aberrationless aerial image light intensity I ₀(x; H) with sensitivity function A _n(x; H) can analytical Calculation obtain:

I ₀(x;h)＝∫∫O(f ₁)O ^*(f ₂)T ₀(f ₁,f ₂;h)×exp[-2πi(f ₁-f ₂)·x]df ₁df ₂, (8)

A _n(x;h)＝∫∫O(f ₁)O ^*(f ₂)B _n(f ₁,f ₂;h)×exp[-2πi(f ₁-f ₂)·x]df ₁df. (9)

Thus aerial image model obtains very big simplification.The simplified model obtained, for given exposure parameter, can calculate fast not containing the zero level aerial image of wave aberration, and the sensitivity matrix of submatrix composition corresponding to each zernike coefficient.

S106, according to the forward model after simplification, calculates the sensitivity matrix of zernike coefficient, wherein, and the matrix that sensitivity matrix is made up of the sub-matrix that each zernike coefficient is corresponding

Specifically, the suitable light intensity of out of focus face h and the changing value of aberrationless light intensity is selected, i.e. light intensity amount of distortion Δ I (x; H), as the observation signal of wave aberration, according to (7) Shi Ke get:

$\mathrm{\ΔI}(x;h)=I(x;h)-I_0(x;h)=\underset{n}{\mathrm{\Σ}}{Z}_n{A}_n(x;h).---\left(10\right)$

Here A _n(x; H) being defined as the sensitivity analysis function detected for wave aberration zernike coefficient, litho machine parameter and mask information being brought into (9) formula, can directly obtaining sensitivity analysis function by calculating.

S108, adopts the conditional number of sensitivity matrix to be optimized as the mask parameters of objective function to mask graph, obtains optimum mask

Because mask graph directly affects sensitivity analysis function, in order to obtain good sensitivity, need to be optimized design to mask graph.The conditional number of described sensitivity matrix is:

F＝cond(A)＝||A||·||A ^-1|| (11)

The conditional number of sensitivity matrix is adopted to be optimized design as the parameter of objective function to mask graph:

$O=\arg *\underset{o}{\min }\left[\mathrm{cond}\left(A\right)\right]=\arg *\underset{o}{\min }\left[\right|\left|A\right||\·|\left|A^{-1}\right|\left|\right].---\left(12\right)$

Wherein, A represents sensitivity matrix { A _n(x; H) }, || || two norms of representing matrix.

The mask parameters optimized comprises the length of side of mask center figure, the length of side of figure, and central figure around and the spacing around between figure.Such as Fig. 2 shows four kinds of example mask figures, wherein Fig. 2 A is a foursquare hole, only have length of side parameter to be optimized, Fig. 2 B, Fig. 2 C, Fig. 2 D have the central figure length of side, around the figure length of side, central figure and surrounding pattern pitch three parameters to optimize simultaneously.The belt restraining multi-parameters optimization algorithm based on Powell is adopted to carry out mask graph optimization in optimizing process.Fig. 3 shows the optimum results of these four kinds of example mask figures, and Fig. 4 shows the conditional number of each figure in Fig. 3, can find out that optimizing process greatly reduces the conditional number of sensitivity matrix.

S110, adopts the mask graph optimized and obtain, and carries out actual exposure measure light intensity at certain out of focus place.

On litho machine, adopt the mask after optimizing to carry out actual exposure, carry out aerial image luminous intensity measurement at out of focus h place, it is for subsequent use that the aerial image light intensity of actual measurement is normalized rear storage.

S112, according to exposing the light intensity value obtained, solves zernike coefficient, obtains the wave aberration reconstructed.

According to formula (10), by measuring h place, the out of focus face aerial image light intensity I (x obtained; And the aberrationless light intensity I calculated h), ₀(x; H), light intensity amount of distortion Δ I (x can be calculated; H), the sensitivity matrix { A by obtaining before _n(x; H) }, zernike coefficient { Z can be solved by least square method _n.When choosing Ze Nike exponent number and aerial image luminosity sampling and counting, should be noted and ensure that luminosity sampling is counted much larger than Ze Nike exponent number, also namely sensitivity matrix is sequency spectrum:

rank(A)＝n, (13)

Here, n is Ze Nike exponent number, can ensure that final system of equations is overdetermined equation like this, thus least square method can be utilized to solve.

As Fig. 5 shows an exemplary wave aberration testing result, there is shown the original zernike coefficient comparative result that there is aberration zernike coefficient and reconstruct and obtain.Fig. 6 shows the error of this example results.

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, all any amendments done within the spirit and principles in the present invention, equivalent replacement and improvement etc., all should be included within protection scope of the present invention.

Claims (3)

1. a measuring method for wave aberration of photo-etching machine projection objective, for carrying out in situ detection to the wave aberration of projection objective, said method comprising the steps of:

Step 102, determine the characterisitic parameter exposed according to actual litho machine process conditions, wherein, characterisitic parameter comprises the numerical aperture of litho machine, and the wavelength of light source, shape and other light sources parameter, this other light sources parameter comprises partial coherence factor σ _out, σ _inand azimuth angle theta;

Step 104, according to the partially coherent image formation Systems Theory of projection aligner, simplify lithographic projection imaging forward model, be specially: adopt the partially coherent image formation system equation based on Thelma Hopkins, wave aberration item in pupil function is launched into zernike polynomial, then intersection transport function is carried out Taylor expansion to single order item, obtain aerial image first order modeling, and then obtain the simplification forward model separated by zernike coefficient;

Step 106, according to the imaging forward model after simplification, calculates the sensitivity matrix of zernike coefficient, wherein, and the matrix that sensitivity matrix is made up of the sub-matrix that each zernike coefficient is corresponding;

Step 108, the conditional number of sensitivity matrix is adopted to be optimized as the parameter of objective function to mask graph, obtain optimum mask, the mask parameters wherein optimized comprises the length of side of mask center figure, the length of side of surrounding figure and central figure and the spacing around between figure, and optimizing process adopts the belt restraining multi-parameters optimization algorithm based on Powell;

Step 110, adopts the mask graph optimized and obtain, carries out actual exposure measurement space as light intensity at certain out of focus place;

Step 112, according to exposing the light intensity value that obtains, solves zernike coefficient, and obtain the wave aberration reconstructed, wherein, described zernike coefficient solves and is specially: according to measuring the defocus space that obtains as light intensity I (x; And the aberrationless light intensity value I calculated h) ₀(x; H), light intensity amount of distortion Δ I (x is calculated; H):

$\mathrm{\ΔI}(x;h)=I(x;h)-I_0(x;h)=\mathrm{\Σ}{Z}_n{A}_n(x;h)$

Sensitivity matrix { the A calculated before utilization _n(x; H) }, zernike coefficient { Z is solved by least square method _n, and when choosing Ze Nike exponent number and aerial image luminosity sampling is counted, ensure that luminosity sampling is counted much larger than Ze Nike exponent number, namely ensure that sensitivity matrix A is sequency spectrum, i.e. rank (A)=n.

2. measuring method according to claim 1, in step 102, the shape of described light source comprises circle, annular, secondary light source and level Four light source.

3. measuring method according to claim 1, in step 108, the conditional number of described sensitivity matrix is:

F＝cond(A)＝||A||·||A ^-1||

Wherein, A represents sensitivity matrix, || two norms of .|| representing matrix.